[1]} propose a BERT-based CMC reader that uses HAM to select and encode dialog history context in three steps.
In the first step, each dialog turn in dialog history, together with the passage and the input question, is encoded into a context vector using BERT. For example, we can construct for each dialog turn an instance sequence, which is a concatenation of the token [CLS], dialog turn \(H\) , input query \(Q\)  and passage \(P\) . We feed the instance into BERT, and take the output representation of [CLS] as the integrated contextual vector of the instance, denoted by \(\mathbf {h}\) .
Let \(\mathbf {h}_k (k = 1,...,K)\)  be the integrated contextual vector of the instance constructed using dialog turn \(H_k\) . Note that the instance for \(H_K\)  is simply the input question \(Q\) .
In the second step, a single-layer feed-forward network is used to compute the weight of each dialog turn with respect to the input question as
\( \alpha _{k} = \text{softmax}(\mathbf {W} \cdot \mathbf {h}_k),\) 
